Question

find the value of logi ? explain it using logarithm of complex numbers equation​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Calculate logz for z=−1−3–√i.

Solution: If z=−1−3–√i, then r=2 and Θ=−2π3. Hence

log(−1−3–√i)=ln2+i(−2π3+2nπ)=ln2+2(n−13)πi

with n∈Z.

The principal value of logz is the value obtained from equation (2) when n=0 and is denoted by Logz. Thus

Logz=lnr+iΘ.

The function Logz is well defined and single-valued when z≠0 and that

logz=Logz+2nπi(n∈Z)

This is reduced to the usual logarithm in calculus when z is a positive real number.